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CHAPTER V.

APPLICATIONS OF ADDITION AND SUBTRACTION.

91. IN a till are $391 in bills, $67.50 in gold, $39.75 in silver, and $2.77 in copper and nickel. How much money is in the till?

92. Starting out with $315.75 in one wallet and $54.37 in another, I pay the grocer $127.38; the butcher, $64.17; the shoemaker, $21.40; the landlord, $50; the tailor, $35. What ought I to have left?

93. On a bill of $753.43, I pay $517.87. How much do I still owe? If I owe $817.87, and have but $637.50, how much do I lack of being able to pay?

94. If a man was born January 1, 1812, how old was he January 1, 1878? How old December 31, 1857?

95. America was discovered in 1492. How many years after its discovery was each of the following events?

Settlement of Florida, 1565; of Virginia, 1607; of Massachusetts, 1620; of Quebec, 1608; French and Indian War, 1756; Declaration of Independence, 1776; inauguration of Washington, 1789; war with England, 1812; Mexican War, 1846; Civil War, 1861.

96. How many days in common years, and in leap-years, between January 1 and March 1? January 4 and April 4?

February 5 and May 5? February 7 and October 7? January 4 and July 4? March 4 and July 4?

97. The sum of two numbers is 3; their difference, 1. What are the numbers? The sum of two numbers is 5; their difference, 1. Required the numbers. What two numbers added together make 8, if the difference of the numbers is 2? If the difference is 0? if 4? if 6?

98. If the minuend is 9874, and remainder 3185, what is the subtrahend? The subtrahend being 7659, and remainder 675.68, what is the minuend?

99. The smaller of two numbers is 7.95764328; their difference is .00087692. What is the larger number?

100. The larger of two numbers is 7.95764328, and their difference is 7.153485. What is the smaller number?

101. A hired man pumps out of my cistern in one hour 243.75 gallons; in the next hour, 227.5 gallons; in 45 minutes more, an additional 137.75 gallons; and the cistern is empty. How much was in it?

102. From what number must I subtract 5 to leave 7? 8 to leave 9? From what number must I subtract 5.1736 to leave 8.1964? 6.231 to leave 9.6648? 74.213 to leave 25.787?

103. What must be subtracted from 1 to leave .5? to leave 0.53? to leave .532? to leave .5236? to leave .5235988?

104. I start on a journey of 3433 miles. The first day I make 428 miles; the second day, 511 miles; the third,

12

APPLICATIONS OF ADDITION AND SUBTRACTION.

29

497 miles; the fourth, 513. How many miles of my journey remained for me at the close of each day? How many miles had I gone at the close of each day?

105. Subtract 76,343 from the sum of 61,932, 51,387, 5193, 4674, and 8199; then subtract 23,657 from the remainder.

106. J. bought a farm and stock for $7633.90; sold off the stock for $305.75; then sold the farm for $7325. What did he lose?

107. If I gave $4375 for my land, and paid for house, barn, sheds, and fences, $2789.50; also $973.75 for horses, cattle, tools, etc.; what did my farm and stock cost?

If I sold part of the land for $675, and some cattle, etc., for $217.50, what may I estimate as the cost of what I have left?

108. Alfred the Great died at the age of 52, a.d. 901. In what year was he born? William the Conqueror began to reign A.D. 1066, and reigned 21 years. In what year did he die? Socrates was born B.C. 469, and died at the age of 70. In what year did he die? Plato was born B.C. 429, and died at the age of 82. In what year did he die? Demosthenes died at the age of 60, B.C. 322. In what year was he born? The battle of Marathon was fought B.C. 490; 560 years later Jerusalem was destroyed by Titus. In what year was Jerusalem destroyed?

109. John has 158 cents, James has 271 cents; James gives John 56 cents. Which has more than the other, and how many more?

CHAPTER VI.

MULTIPLICATION.

110. A ST. ANDREW's cross (X) between two numbers means that one of the numbers is to be repeated as many times as is indicated by the other number. The number to be repeated is called the multiplicand; the number which shows how many times the multiplicand is to be repeated is called the multiplier; and the result is called the product.

The sign (X) is read times, or multiplied by, according as the multiplier precedes or follows the multiplicand. Thus, 5 × 4 cents = 20 cents is read, five times four cents equals twenty cents; but, 4 cents x 5 = 20 cents is read: four cents multiplied by five equals twenty cents.

111. The multiplier and multiplicand are often called factors of the product. The product of two or more factors is the same in whatever order they are taken. Thus, 3 × 4 = 4 × 3. The dots in the margin, read horizontally, make 3 fours; read vertically, make 4 threes.

112. The sign × cannot extend its power, forward or backward, beyond a or, without the aid of a parenthesis. To illustrate :

+

2+3x4-1=13;

(2+3)x4-1= 19;

2+3x (4-1) = 11; (2+3) x (4-1)=15.

113. The products, in all cases in which neither factor exceeds ten, should be thoroughly committed to memory. They will be found in the following table:

1

2

3

4

246

MULTIPLICATION TABLE.

3 4

5

6

6 7 8 9 10 11 12

8 10 12 14 16 18 20 22 24

9 12 15 18 21 24 27 30 33 36

8 12 16 20 24 28 32 36 40 44 48 5 10 15 20 25 30 35 40 45 50 55 60 6 12 18 24 30 36 42 48 54 60 66 72 7 14 21 28 35 42 49 56 63 70 77 84 8 16 24 32 40 48 56 64 72 80 88 96 18 27 36 45 54 63 72 81 90 99 108

9

114. In the above table, take the multiplier in the upper line, the multiplicand in the left-hand column; the products will be found directly under the multiplier, and opposite the multiplicand; as, 12 × 7 is 84.*

115. To multiply any multiplicand by a multiplier less than 13, the work may be written as in the margin. Beginning at the right, 4 × 8 is 32; the 2 is written, and the 3 carried mentally and added to 4 x 6, making 27; and the process is thus continued to the left.

12 x 896; 12 x 672, and 9 makes 81; 12 x 672; 12 x 336, and 7 makes 43: 12 × 2 = 24, and 4 makes 28; 12 × 2=24, and 2 makes 26.

2.236068

4

8.944272

2.236068

12

26.832816

The table should be learned, not by lines but by squares; that is, first learn 2 × 2, 2 × 3 and 3 × 2, 3 × 3; next learn 2 × 4, 3 × 4, 4 × 2, 4 × 3, 4X4; thirdly, 2 × 5, 3 × 5, 4 × 5, 5 X 2, 5 X 3, 54, 5×5; fourthly, all products under 36, etc.

The cards referred to in the footnote to 43 may be advantageously used for practice in multiplying two digits. Shuffle them, and pass them in couples from one hand to the other, naming the two factors, while the pupil names the products.

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